AI 中文总结
研究加法阿贝尔半群有限子集\(h\)重和集大小问题，证明整数有限集与\(n\)维格点有限集的“和集大小范围”相同，并探讨用格点计算和集大小集合是否比整数更高效。
AI 中文摘要
加法数论中的一个核心问题是理解加法阿贝尔半群有限子集的\(h\)重和的大小集合。本文证明了整数有限集和\(n\)维格点有限集的“和集大小范围”是相同的。相关几何问题是确定使用格点计算这些和集大小集合是否比使用整数更有效。
英文摘要
A central problem in additive number theory is to understand the set of sizes of $h$-fold sums of finite subsets of an additive abelian semigroup. It is proved that the "range of sumset sizes'' is the same for finite sets of integers and for finite sets of $n$-dimensional lattice points. The associated geometrical problem is to determine if these sumset size sets can be computed more efficiently with lattice points than with integers.
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